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Neighbouring numbers in real draws: why 52.9% is normal
You look at the winning numbers and see 23 and 24 side by side. It feels staged. A result like 3-17-29-34-41-44, evenly scattered, feels more like what "random" should look like. This page counts instead of feeling. The chance that a six-number draw from 1 to 45 contains at least one neighbouring pair is 52.9%, and in the 1,247 recorded Lotto 6/45 rounds the share was 51.8%. Neighbouring numbers appear in more than half of all draws, yet many people find them suspicious.
Counting the draws that contain a neighbouring pair
There are C(45,6) = 8,145,060 ways to pick six distinct numbers. A "neighbouring pair" is two chosen numbers that differ by 1, like 23 and 24. The set {4, 5, 6, 20, 31, 40} contains two pairs (4-5 and 5-6). How many sets contain exactly j pairs?
Line the six numbers up in order. There are five places where two numbers can sit next to each other, and exactly j of them must be adjacent: that is C(5,j) choices. Glue each adjacent pair into one block. You now place 6 − j blocks onto 45 − j positions so that no two blocks touch. Placing k non-touching items onto N positions can be done in C(N − k + 1, k) ways; with N = 45 − j and k = 6 − j this is C(40, 6 − j). So the number of draws with exactly j neighbouring pairs is C(5,j) × C(40, 6 − j). Summing over j gives C(45,6) by Vandermonde's identity, which confirms nothing was missed.
| Neighbouring pairs | Draws | Probability | Expected in 1,247 rounds | Observed rounds |
|---|---|---|---|---|
| 0 (all apart) | 3,838,380 | 47.13% | 587.7 | 601 |
| 1 | 3,290,040 | 40.39% | 503.7 | 490 |
| 2 | 913,900 | 11.22% | 139.9 | 134 |
| 3 | 98,800 | 1.213% | 15.1 | 20 |
| 4 | 3,900 | 0.0479% | 0.6 | 2 |
| 5 (six in a row) | 40 | 0.00049% | 0.0 | 0 |
The draws with all six numbers apart number C(40,6) = 3,838,380, or 47.13%. Everything else, 52.87%, contains at least one pair. Only 40 draws consist of six consecutive numbers (1-2-3-4-5-6, 2-3-4-5-6-7, and so on). That is about 1 in 200,000, but each of those 40 draws still has the same 1-in-8,145,060 chance as any other draw.
Did the real 1,247 rounds follow the table?
I counted the six main numbers of every round from 1 to 1,247 the same way. 646 rounds (51.8%) contain at least one neighbouring pair, against 52.9% expected. Pooling three or more pairs into one row and running a chi-square test gives 3.43 on 3 degrees of freedom, p ≈ 0.33: well inside normal fluctuation. The largest gap between expected and observed is in the three-pair row (15.1 expected, 20 observed), a difference chance produces regularly.
Runs of three or more consecutive numbers were checked too. Draws containing something like 7-8-9 number 458,420 of 8,145,060 (5.63%); in the records there were 68 of 1,247 rounds (5.45%) against an expected 70.2. Four or more in a row has a probability of 0.40%, an expected 5.0 rounds, and 6 observed. The longest run in the whole history is four numbers.
How often last round's numbers come back
A related remark is "last week's number came up again". For two consecutive rounds, the chance that k of the new six numbers were among the previous six is C(6,k) × C(39, 6 − k) / C(45,6), with an average of 6 × 6/45 = 0.8 repeated numbers. Over the 1,246 pairs of neighbouring rounds the average was 0.827.
| Shared numbers | Expected | Observed |
|---|---|---|
| 0 | 499.1 | 481 |
| 1 | 528.5 | 528 |
| 2 | 188.7 | 211 |
| 3 | 28.0 | 24 |
| 4 or more | 1.7 | 2 |
In theory 40.1% of rounds share no number with the previous one and 59.9% share at least one; the records show 38.6% and 61.4%. "One of last week's numbers came back" is ordinary, not strange.
Run it yourself
The tool below repeats random Lotto 6/45 draws and counts neighbouring pairs. The more draws you ask for, the closer the shares get to the exact column above.
What about other lotteries?
Put j = 0 into the same formula (exactly j pairs: C(m − 1, j) × C(n − m + 1, m − j)) and you get the share of draws with no neighbours at all. A larger number of picks or a smaller pool makes neighbours more likely. Japan's Loto 7 picks 7 of 37, so a draw contains at least one neighbouring pair with probability 74.5%. The feeling that "no neighbours is normal" is wrong by a different amount in each game.
| Lottery | Picks | At least one neighbouring pair |
|---|---|---|
| Lotto 6/45 (Korea) | 6 of 45 | 52.87% |
| Loto 6 (Japan) | 6 of 43 | 54.72% |
| Loto 7 (Japan) | 7 of 37 | 74.46% |
| EuroMillions (main numbers) | 5 of 50 | 35.30% |
| UK Lotto | 6 of 59 | 42.68% |
| SuperEnalotto | 6 of 90 | 29.76% |
With a pool of 90 numbers, SuperEnalotto produces a neighbouring pair in fewer than one draw in three. The table is computed from each game's number format only; it has not been checked against the actual draw history of those games.
Why neighbours look "staged"
Neighbouring numbers feel odd not because they are rare but because they stand out. People are good at noticing shapes that look like rules. Seeing 23 beside 24 registers at once; 17-31-38 forms no pattern and is forgotten. What is noticed is remembered, and what is remembered gets treated as frequent. The table above corrects that estimate: a draw without any neighbours is actually the smaller half.
There is a second reason: many people equate "random" with "evenly spread". Real random results contain clumps and gaps. In the same way a hundred fair coin flips contain a run of six or more identical results with probability above 80% (the runs discussed in the gambler's fallacy). Neighbouring numbers are the same illusion in another costume.
What this means when choosing numbers
A single ticket's jackpot chance is 1 in 8,145,060 whether it contains neighbours or not. 1-2-3-4-5-6 and six scattered numbers have identical chances. What this page measured is the shape of drawn results, not which numbers people choose. This data cannot say whether buyers avoid or favour neighbouring numbers, so the page does not conclude "avoid them because they are shared" or "pick them because others avoid them". How sharing a jackpot depends on popular combinations is examined with real winner counts in Same odds, different split risk.
Questions that come up
Is it rigged if two neighbouring pairs show up? Draws with two or more pairs have a probability of 12.5% (11.22 + 1.21 + 0.05 + 0.0005) and the records contain 156 of them (12.5%). That is about one draw in eight.
What if the bonus number is included? This page used the six main numbers only. Counting all seven balls makes a neighbouring pair slightly more likely, but the bonus ball is a separate ball drawn after the main numbers, so the counting rule changes.
Do other lotteries work the same way? The formula is general. For m numbers chosen from n, the number of choices with exactly j neighbouring pairs is C(m − 1, j) × C(n − m + 1, m − j). The share of draws with at least one pair rises as the pool gets smaller or the number of picks grows.
What this count does not prove
It does not prove a draw is fair. It shows only that the records are not far from the theory, and the limits of using statistics to build evidence of fairness are described in How a lottery draw is kept fair. The shape of past results also says nothing about the next round. That the pair counts and the overlap with the previous round match the theory is consistent with the assumption of this page that rounds do not influence each other. The data are the results published by Donghaeng Lottery for rounds 1 to 1,247, collected by hand; only aggregates are published.
LottoFlick is independent and not an official lottery operator. Numbers are random and cannot be predicted.
Sources and verification
- Donghaeng Lottery: Lotto 6/45 round results, rounds 1–1247 (collected by hand 2026-10-24) — verified
- LottoFlick calculation: exact counts of draws by number of neighbouring pairs, observed rounds, chi-square test, overlap with the previous round — computed by LottoFlick